Answer:
The answer is below
Step-by-step explanation:
The compound interest is given by the formula:
[tex]A=P(1+\frac{r}{n} )^{nt}[/tex]
Where A is the final amount, p is the principal (initial amount), r is the rate, t is the number of period and n is the number of times it was compounded per period.
Given that:
The interest is compounded yearly, i.e n = 1, for 1 year, t = 1, the compound interest is Rs 450 i.e A = 450. Therefore:
[tex]450=P(1+\frac{r}{1} )^{1*1}=P(1+r)\\450=P(1+r).\ .\ .\ (1)[/tex]
For 2 year, t = 2, the compound interest is Rs 945 i.e A = 945. Therefore:
[tex]945=P(1+\frac{r}{1} )^{1*2}=P(1+r)^2\\945=P(1+r)^2.\ .\ .\ (2)[/tex]
Dividing equation 2 by equation 1 gives:
2.1 = 1 + r
r = 2.1 - 1 = 1.1
r = 1.1
Put r = 1.1 in 450 = P(1 + r)
450 = P(1 + 1.1)
450 = 1.11P
P = 405.4
Therefore the rate is 1.1 = 110% and P = Rs 405.4
